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  • 1. Ambat, Sooraj K.
    et al.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Hari, K. V. S.
    Progressive fusion of reconstruction algorithms for low latency applications in compressed sensing2014In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 97, p. 146-151Article in journal (Refereed)
    Abstract [en]

    Recently, it has been shown that fusion of the estimates of a set of sparse recovery algorithms result in an estimate better than the best estimate in the set, especially when the number of measurements is very limited. Though these schemes provide better sparse signal recovery performance, the higher computational requirement makes it less attractive for low latency applications. To alleviate this drawback, in this paper, we develop a progressive fusion based scheme for low latency applications in compressed sensing. In progressive fusion, the estimates of the participating algorithms are fused progressively according to the availability of estimates. The availability of estimates depends on computational complexity of the participating algorithms, in turn on their latency requirement. Unlike the other fusion algorithms, the proposed progressive fusion algorithm provides quick interim results and successive refinements during the fusion process, which is highly desirable in low latency applications. We analyse the developed scheme by providing sufficient conditions for improvement of CS reconstruction quality and show the practical efficacy by numerical experiments using synthetic and real-world data.

  • 2. Carlsson, B
    et al.
    Händel, Peter
    Uppsala universitet.
    A NOTCH FILTER BASED ON RECURSIVE LEAST-SQUARES MODELING1994In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 35, no 3, p. 231-239Article in journal (Refereed)
    Abstract [en]

    This paper presents a notch filter based on recursive least-squares sinusoidal modelling. This gives analytical insight both into least-squares modelling of sine waves in noise and the use of constrained notch filters. Especially, the derived filter corresponds to a commonly used notch filter with constrained poles and zeros.

  • 3.
    Chatterjee, Saikat
    et al.
    Indian Institute of Science.
    Sreenivas, T.V.
    Indian Institute of Science.
    Optimum switched split vector quantization of LSF parameters2008In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 88, no 6, p. 1528-1538Article in journal (Refereed)
  • 4.
    Ekblad, Ulf
    et al.
    KTH, Superseded Departments, Physics.
    Kinser, J M
    Theoretical foundation of the intersecting cortical model and its use for change detection of aircraft, cars, and nuclear explosion tests2004In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 84, no 7, p. 1131-1146Article in journal (Refereed)
    Abstract [en]

    The intersecting cortical model (ICM) is a model based on neural network techniques especially designed for image processing. It was derived from several visual cortex models and is basically the intersection of these models, i.e. the common elements amongst these models. The theoretical foundation of the ICM is given and it is shown how the ICM can be derived as a reduced set of equations of the pulse-coupled neural network based upon models proposed by Eckhorn and Reitboeck. Tests of the ICM are presented: one on a series of images of an aircraft moving in the sky; two on car detection; and one on preparations of underground nuclear explosions. The ICM is shown here, in a few examples, to be useful in imagery change detection: aircraft moving against a homogeneous background without precise geometric matching; car on a road; two cars moving in an urban setting without precise geometric matching; and for a linear structure in a complex background. The ICM can be used when the moving objects are not too small and the background is not too difficult. Changes involving larger linear structures can be detected even if the background is not homogeneous.

  • 5.
    Enqvist, Per
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    On the simultaneous realization problem - Markov-parameter and covariance interpolation2006In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 86, no 10, p. 3043-3054Article in journal (Refereed)
    Abstract [en]

    An efficient algorithm for determining the unique minimal and stable realization of a window of Markov parameters and covariances is derived. The main difference compared to the Q-Markov COVER theory is that here we let the variance of the input noise be a variable, thus avoiding a certain data consistency criterion. First, it is shown that maximizing the input variance of the realization over all interpolants yields a minimal degree solution-a result closely related to maximum entropy. Secondly, the state space approach of the Q-Markov COVER theory is used for analyzing the stability and structure of the realization by straightforward application of familiar realization theory concepts, in particular the occurrence of singular spectral measures is characterized.

  • 6.
    Gholami, Mohammad Reza
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ström, Erik G.
    Wymeersch, Henk
    Rydström, Mats
    On geometric upper bounds for positioning algorithms in wireless sensor networks2015In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 111, p. 179-193Article in journal (Refereed)
    Abstract [en]

    This paper studies the possibility of upper bounding the position error for range-based positioning algorithms in wireless sensor networks. In this study, we argue that in certain situations when the measured distances between sensor nodes have positive errors, e.g., in non-line-of-sight (NLOS) conditions, the target node is confined to a closed bounded convex set (a feasible set) which can be derived from the measurements. Then, we formulate two classes of geometric upper bounds with respect to the feasible set. If an estimate is available, either feasible or infeasible, the position error can be upper bounded as the maximum distance between the estimate and any point in the feasible set (the first bound). Alternatively, if an estimate given by a positioning algorithm is always feasible, the maximum length of the feasible set is an upper bound on position error (the second bound). These bounds are formulated as nonconvex optimization problems. To progress, we relax the nonconvex problems and obtain convex problems, which can be efficiently solved. Simulation results show that the proposed bounds are reasonably tight in many situations, especially for NLOS conditions.

  • 7.
    Gudmundson, Erik
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Signal Processing.
    Jakobsson, Andreas
    Jensen, Jorgen A.
    Stoica, Petre
    Blood velocity estimation using ultrasound and spectral iterative adaptive approaches2011In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 91, no 5, p. 1275-1283Article in journal (Refereed)
    Abstract [en]

    This paper proposes two novel iterative data-adaptive spectral estimation techniques for blood velocity estimation using medical ultrasound scanners. The techniques make no assumption on the sampling pattern of the emissions or the depth samples, allowing for duplex mode transmissions where B-mode images are interleaved with the Doppler emissions. Furthermore, the techniques are shown, using both simplified and more realistic Field II simulations as well as in vivo data, to outperform current state-of-the-art techniques, allowing for accurate estimation of the blood velocity spectrum using only 30% of the transmissions, thereby allowing for the examination of two separate vessel regions while retaining an adequate updating rate of the B-mode images. In addition, the proposed methods also allow for more flexible transmission patterns, as well as exhibit fewer spectral artifacts as compared to earlier techniques.

  • 8.
    Helgason, Hannes
    et al.
    KTH, School of Electrical Engineering (EES), Sound and Image Processing.
    Pipiras, Vladas
    Abry, Patrice
    Synthesis of multivariate stationary series with prescribed marginal distributions and covariance using circulant matrix embedding2011In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 91, no 8, p. 1741-1758Article in journal (Refereed)
    Abstract [en]

    The problem of synthesizing multivariate stationary series Y[n] = (Y-1[n],...,Y-p[n](T), n is an element of Z, with prescribed non-Gaussian marginal distributions, and a targeted covariance structure, is addressed. The focus is on constructions based on a memoryless transformation Y-p[n] = f(p)(X-p[n]) of a multivariate stationary Gaussian series X[n] = (X-1[n],...,X-p[n])(T). The mapping between the targeted covariance and that of the Gaussian series is expressed via Hermite expansions. The various choices of the transforms f(p) for a prescribed marginal distribution are discussed in a comprehensive manner. The interplay between the targeted marginal distributions, the choice of the transforms f(p), and on the resulting reachability of the targeted covariance, is discussed theoretically and illustrated on examples. Also, an original practical procedure warranting positive definiteness for the transformed covariance at the price of approximating the targeted covariance is proposed, based on a simple and natural modification of the popular circulant matrix embedding technique. The applications of the proposed methodology are also discussed in the context of network traffic modeling. MATIAB codes implementing the proposed synthesis procedure are publicly available at http://www.hermir.org.

  • 9.
    Händel, Peter
    Uppsala universitet.
    High-order Yule-Walker estimation of the parameters of exponentially damped cisoids in noise1993In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 32, no 3, p. 315-328Article in journal (Refereed)
    Abstract [en]

    An approach for the estimation of the frequencies and damping factors of exponentially damped cisoids (complex sinusoids) is presented. The method may be seen as an extension of the method of backward linear prediction and singular value decomposition of Kumaresan and Tufts to the second-order statistics domain. The proposed estimator is interpreted as a high-order Yule-Walker (HOYW) method using a data based covariance matrix. The HOYW method is analysed at high SNR where closed-form expressions for the accuracy of the estimates are derived. By Monte Carlo simulations the HOYW method is applied to data consisting of one and two damped cisoids in additive white noise. The simulation results are compared with the results using the Kumaresan and Tufts method, with the Cramer-Rao bound, and with the derived theoretical results. The method is not statistically efficient, but the comparison shows that the HOYW method outperforms the method of Kumaresan and Tufts in terms of accuracy versus algorithmic complexity and in terms of precision in the cases considered. Due to the above properties the method is suitable to provide fast initial estimates for nonlinear search methods.

  • 10.
    Händel, Peter
    et al.
    Uppsala universitet.
    Eriksson, A.
    Wigren, T.
    Performance analysis of a correlation based single tone frequency estimator1995In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 44, no 2, p. 223-231Article in journal (Refereed)
    Abstract [en]

    This paper analyzes the frequency error variance of a low complexity single tone frequency estimator based on sample correlations of the input data. In the high SNR scenario it is analytically shown that the accuracy of a properly tuned algorithm is nearly optimal, i.e. nearly attains the Cramer-Rao lower bound. For low SNR the statistical efficiency of the algorithm is degraded, but it is analytically proven that for a large number of samples the error variance attains the lower bound for this class of estimators.

  • 11.
    Händel, Peter
    et al.
    Uppsala universitet.
    Stoica, P.
    Söderström, T.
    Asymptotic variance of the AR spectral estimator for noisy sinusoidal data1994In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 35, no 2, p. 131-139Article in journal (Refereed)
    Abstract [en]

    In this paper the autoregressive (AR) spectral estimator is analyzed in the case of noisy sinusoidal data. An expression for the large-sample normalized variance is derived and studied in detail for increasing model order. In particular, a very simple formula is derived for the asymptotic (in both number of observed data and model order) normalized variance, which confirms a conjecture made by Sakai.

  • 12.
    Händel, Peter
    et al.
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Tichavsky, P.
    Asymptotic noise gain of polynomial predictors1997In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 62, no 2, p. 247-250Article in journal (Refereed)
    Abstract [en]

    Finite impulse response filters for the prediction of polynomial signals are considered. An expression for the asymptotic noise gain (as the filter length increases without bound) is derived. It is shown that the asymptotic noise gain only depends on the polynomial order - in particular, it is independent of the prediction horizon. It is also shown that the noise gain forms a non-increasing sequence for increasing filter lengths. Numerical results that lend support to the theoretical findings are included.

  • 13. Ilic, Nemanja
    et al.
    Stankovic, Srdjan S.
    Stankovic, Milos S.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Consensus based distributed change detection using Generalized Likelihood Ratio methodology2012In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 92, no 7, p. 1715-1728Article in journal (Refereed)
    Abstract [en]

    In this paper a novel distributed algorithm derived from the Generalized Likelihood Ratio is proposed for real time change detection using sensor networks. The algorithm is based on a combination of recursively generated local statistics and a global consensus strategy, and does not require any fusion center. The problem of detection of an unknown change in the mean of an observed random process is discussed and the performance of the algorithm is analyzed in the sense of a measure of the error with respect to the corresponding centralized algorithm. The analysis encompasses asymmetric constant and randomly time varying matrices describing communications in the network, as well as constant and time varying forgetting factors in the underlying recursions. An analogous algorithm for detection of an unknown change in the variance is also proposed. Simulation results illustrate characteristic properties of the algorithms including detection performance in terms of detection delay and false alarm rate. They also show that the theoretical analysis connected to the problem of detecting change in the mean can be extended to the problem of detecting change in the variance.

  • 14.
    Jansson, Magnus
    et al.
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    A Linear Regression Approach to State-Space Subspace System Identification1996In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 52, no 2, p. 103-129Article in journal (Refereed)
    Abstract [en]

    Recently, state-space subspace system identification (4SID) has been suggested as an alternative to the more traditional prediction error system identification. The aim of this paper is to analyze the connections between these two different approaches to system identification. The conclusion is that 4SID can be viewed as a linear regression multistep-ahead prediction error method with certain rank constraints. This allows us to describe 4SID methods within the standard framework of system identification and linear regression estimation. For example, this observation is used to compare different cost-functions which occur rather implicitly in the ordinary framework of 4SID. From the cost-functions, estimates of the extended observability matrix are derived and related to previous work. Based on the estimates of the observability matrix, the asymptotic properties of two pole estimators, namely the shift invariance method and a weighted subspace fitting method, are analyzed. Expressions for the asymptotic variances of the pole estimation error are given. From these expressions, difficulties in choosing user-specified parameters are pointed out. Furthermore, it is found that a row-weighting in the subspace estimation step does not affect the pole estimation error asymptotically.

  • 15.
    Katselis, Dimitrios
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Frequency smoothing gains in preamble-based channel estimation for multicarrier systems2013In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 93, no 9, p. 2777-2782Article in journal (Refereed)
    Abstract [en]

    In this paper, the problem of least-squares (LS) preamble-based channel estimation in multicarrier systems under a deterministic channel assumption is revisited. The analysis is presented for the filterbank multicarrier offset quadrature amplitude modulation (FBMC/OQAM) system, although the derived results hold unchanged for the cyclic prefixed orthogonal frequency division multiplexing (CP-OFDM) system, as well. Assuming independent noise disturbances per subcarrier, we show that frequency-domain smoothing techniques can be used to improve the mean square error (MSE) performance. Depending on the number of subcarriers, the choice of smoothing may be different. We also present the time-domain formulation of the frequency-domain smoothing. Based on this formulation, we show that frequency-domain smoothing techniques can minimize the variance of the LS channel estimator, while they can further reduce its MSE by trading bias for variance. Simulations are given to support the derived results.

  • 16. Kofidis, Eleftherios
    et al.
    Katselis, Dimitrios
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Automatic Control.
    Rontogiannis, Athanasios
    Theodoridis, Sergios
    Preamble-based channel estimation in OFDM/OQAM systems: A review2013In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 93, no 7, p. 2038-2054Article, review/survey (Refereed)
    Abstract [en]

    Filter bank-based multicarrier communications (FBMC) have recently attracted increased interest in both wired (e.g., xDSL, PLC) and wireless (e.g., cognitive radio) applications, due to their enhanced flexibility, higher spectral efficiency, and better spectral containment compared to conventional OFDM. A particular type of FBMC, the so-called FBMC/OQAM or OFDM/OQAM system, consisting of pulse shaped OFDM carrying offset QAM (OQAM) symbols, has received increasing attention due to, among other features, its higher spectral efficiency and implementation simplicity. It suffers, however, from an imaginary inter-carrier/inter-symbol interference that complicates signal processing tasks such as channel estimation. This paper focuses on channel estimation for OFDM/OQAM systems based on a known preamble. A review of the existing preamble structures and associated channel estimation methods is given, for both single- (SISO) and multiple-antenna (MIMO) systems. The various preambles are compared via simulations in both mildly and highly frequency selective channels.

  • 17. Koochakzadeh, Ali
    et al.
    Malek-Mohammadi, Mohammadreza
    Babaie-Zadeh, Massoud
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Multi-antenna assisted spectrum sensing in spatially correlated noise environments2015In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 108, p. 69-76Article in journal (Refereed)
    Abstract [en]

    A significant challenge in spectrum sensing is to lessen the signal to noise ratio needed to detect the presence of primary users while the noise level may also be unknown. To meet this challenge, multi-antenna based techniques possess a greater efficiency compared to other algorithms. In a typical compact multi-antenna system, due to small interelement spacing, mutual coupling between thermal noises of adjacent receivers is significant. In this paper, unlike most of the spectrum sensing algorithms which assume spatially uncorrelated noise, the noises on the adjacent antennas can have arbitrary correlations. Also, in contrast to some other algorithms, no prior assumption is made on the temporal properties of the signals. We exploit low-rank/sparse matrix decomposition algorithms to obtain an estimate of noise and received source covariance matrices. Given these estimates, a Semi-Constant False Alarm Rate (S-CFAR) detector, in which the probability of false alarm is constant over the scaling of the noise covariance matrix, to examine the presence of primary users is proposed. In order to analyze the efficiency of our algorithm, we derive approximate probability of detection. Numerical simulations show that the proposed algorithm consistently and considerably outperforms state-of-the-art multiantenna based spectrum sensing algorithms.

  • 18. Koski, Timo
    The Wold isomorphism for cyclostationary sequences2004In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 84, no 5, p. 813-824Article in journal (Refereed)
    Abstract [en]

    In 1948 Wold introduced an isometric isomorphism between a Hilbert (linear) space formed from the weighted shifts of a numerical sequence and a suitable Hilbert space of values of a second-order stochastic sequence. Motivated by a recent resurrection of the idea in the context of cyclostationary sequences and processes, we present the details of the Wold isomorphism between cyclostationary stochastic sequences and cyclostationary numerical sequences. We show how Hilbert-space representations of cyclostationary sequences are interpreted in the case of numerical CS sequences.

  • 19.
    Li, Kezhi
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Medical Research Council, Imperial College London, White City, United Kingdom.
    Sundin, Martin
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jansson, Magnus
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Alternating strategies with internal ADMM for low-rank matrix reconstruction2016In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 121, p. 153-159Article in journal (Refereed)
    Abstract [en]

    This paper focuses on the problem of reconstructing low-rank matrices from underdetermined measurements using alternating optimization strategies. We endeavour to combine an alternating least-squares based estimation strategy with ideas from the alternating direction method of multipliers (ADMM) to recover low-rank matrices with linear parameterized structures, such as Hankel matrices. The use of ADMM helps to improve the estimate in each iteration due to its capability of incorporating information about the direction of estimates achieved in previous iterations. We show that merging these two alternating strategies leads to a better performance and less consumed time than the existing alternating least squares (ALS) strategy. The improved performance is verified via numerical simulations with varying sampling rates and real applications.

  • 20. Ma, Zhanyu
    et al.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Kleijn, W. Bastiaan
    Guo, Jun
    Dirichlet mixture modeling to estimate an empirical lower bound for LSF quantization2014In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 104, p. 291-295Article in journal (Refereed)
    Abstract [en]

    The line spectral frequencies (LSFs) are commonly used for the linear predictive/autoregressive model in speech and audio coding. Recently, probability density function (PDF)-optimized vector quantization (VQ) has been studied intensively for quantization of LSF parameters. In this paper, we study the VQ performance bound of the LSF parameters. The LSF parameters are transformed to the Delta LSF domain and the underlying distribution of the Delta LSF parameters is modeled by a Dirichlet mixture model (DMM) with a finite number of mixture components. The quantization distortion, in terms of the mean squared error (MSE), is calculated with high rate theory. For LSF quantization, the mapping relation between the perceptually motivated log spectral distortion (LSD) and the MSE is empirically approximated by a polynomial. With this mapping function, the minimum required bit rate (an empirical lower bound) for transparent coding of the LSF under DMM modeling is derived.

  • 21. Ma, Zhanyu
    et al.
    Taghia, Jalil
    Kleijn, W. Bastiaan
    Leijon, Arne
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Guo, Jun
    Line spectral frequencies modeling by a mixture of von Mises-Fisher distributions2015In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 114, p. 219-224Article in journal (Refereed)
    Abstract [en]

    Efficient quantization of the linear predictive coding (LPC) parameters plays a key role in parametric speech coding. The line spectral frequency (LSF) representation of the LPC parameters has found its applications in speech model quantization. In practical implementations of vector quantization (VQ), probability density function optimized VQ has been shown to be more efficient than the VQ based on training data. In this paper, we present the LSF parameters by a unit vector form, which has directional characteristics. The underlying distribution of this unit vector variable is modeled by a von Mises-Fisher mixture model (VMM). An optimal inter-component bit allocation strategy is proposed based on high rate theory and a distortion-rate (D-R) relation is derived for the VMM based-VQ (VVQ). Experimental results show that the VVQ outperforms the recently introduced Dirichlet mixture model-based VQ and the conventional Gaussian mixture model-based VQ in terms of modeling performance and D-R relation.

  • 22. Malek Mohammadi, Mohammadreza
    et al.
    Babaie-Zadeh, Massoud
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Performance Guaranteesfor Schatten-p Quasi-Norm Minimization in Recovery of Low-Rank Matrices2015In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 114, p. 225-230Article in journal (Refereed)
    Abstract [en]

    We address some theoretical guarantees for Schatten-p   quasi-norm minimization (p∈(0,1]p∈(0,1]) in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measurement operator, we provide a sufficient condition for exact recovery of low-rank matrices. This condition guarantees unique recovery of matrices of ranks equal or larger than what is guaranteed by nuclear norm minimization. Secondly, this sufficient condition leads to a theorem proving that all restricted isometry property (RIP) based sufficient conditions for pℓp quasi-norm minimization generalize to Schatten-p quasi-norm minimization. Based on this theorem, we provide a few RIP-based recovery conditions.

  • 23.
    Malek Mohammadi, Mohammadreza
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jansson, Magnus
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Information Science and Engineering.
    Babaie-Zadeh, Massoud
    Upper bounds on the error of sparse vector and low-rank matrix recovery2016In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 120, p. 249-254Article in journal (Refereed)
    Abstract [en]

    Suppose that a solution x to an underdetermined linear system b=Ax is given. x is approximately sparse meaning that it has a few large components compared to other small entries. However, the total number of nonzero components of x is large enough to violate any condition for the uniqueness of the sparsest solution. On the other hand, if only the dominant components are considered, then it will satisfy the uniqueness conditions. One intuitively expects that x should not be far from the true sparse solution x0. It was already shown that this intuition is the case by providing upper bounds on ||x-x0|| which are functions of the magnitudes of small components of x but independent from x0. In this paper, we tighten one of the available bounds on ||x-x0|| and extend this result to the case that b is perturbed by noise. Additionally, we generalize the upper bounds to the low-rank matrix recovery problem.

  • 24.
    Nader, Charles
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. University of Gävle, Sweden; Vrije Universiteit Brussel,, Belgium.
    Björsell, Niclas
    University of Gävle, Sweden.
    Händel, Peter
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Unfolding the Frequency Spectrum for Undersampled Wideband Data2011In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 91, no 5, p. 1347-1350Article in journal (Refereed)
    Abstract [en]

    In this letter, we discuss the problem of unfolding the frequency spectrum for undersampled wideband data. The problem is of relevance to state-of-the-art radio frequency measurement systems, which capture repetitive waveform based on a sampling rate that violates the Nyquist constraint. The problem is presented in a compact form by the inclusion of a complex operator called the CN operator. The ease-of-use problem formulation eliminates the ambiguity caused by folded frequency spectra, in particular those with lines standing on multiples of the Nyquist frequency that are captured with erroneous amplitude and phase values.

  • 25.
    Stoica, Petre
    et al.
    Division of Systems and Control, Department of Information Technology, Uppsala University, Uppsala, Sweden.
    Jansson, Magnus
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On maximum likelihood estimation in factor analysis-An algebraic derivation2009In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 89, no 6, p. 1260-1262Article in journal (Refereed)
    Abstract [en]

    The maximum likelihood estimate in factor analysis is typically obtained as the solution of the stationary point equation of the likelihood function. This type of derivation suffers from two problems: it is rather cumbersome and, in fact, it is incomplete as it does not include a proof that the so-obtained estimate is indeed a global maximum point of the likelihood function. In this note we present a simple algebraic derivation of the maximum likelihood estimate in factor models with spherical noise that applies to the general complex-valued data case.

  • 26.
    Stoica, Petre
    et al.
    Systems and Control Group, Uppsala University, P.O. Box 27, S-751 03 Uppsala, Sweden.
    Ottersten, Björn
    KTH, Superseded Departments, Signals, Sensors and Systems.
    The evil of superefficiency1996In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 55, no 1, p. 133-136Article in journal (Refereed)
    Abstract [en]

    We discuss the intriguing notion of statistical superefficiency in a straightforward manner with a minimum of formality. We point out that for any given parameter estimator there exist other estimators which have a strictly lower asymptotic variance and hence are statistically more efficient than the former. In particular, if the former estimator was statistically efficient (in the sense that its asymptotic variance was equal to the Cramer-Rao bound) then the latter estimators could be called ''superefficient''. Among others, the phenomenon of superefficiency implies that asymptotically there exists no uniformly minimum-variance parameter estimator.

  • 27.
    Sundman, Dennis
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Distributed greedy pursuit algorithms2014In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 105, p. 298-315Article in journal (Refereed)
    Abstract [en]

    For compressed sensing over arbitrarily connected networks, we consider the problem of estimating underlying sparse signals in a distributed manner. We introduce a new signal model that helps to describe inter-signal correlation among connected nodes. Based on this signal model along with a brief survey of existing greedy algorithms, we develop distributed greedy algorithms with low communication overhead. Incorporating appropriate modifications, we design two new distributed algorithms where the local algorithms are based on appropriately modified existing orthogonal matching pursuit and subspace pursuit. Further, by combining advantages of these two local algorithms, we design a new greedy algorithm that is well suited for a distributed scenario. By extensive simulations we demonstrate that the new algorithms in a sparsely connected network provide good performance, close to the performance of a centralized greedy solution.

  • 28. Tichavsky, P.
    et al.
    Händel, Peter
    Recursive estimation of frequencies and frequency rates of multiple cisoids in noise1997In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 58, no 2, p. 117-129Article in journal (Refereed)
    Abstract [en]

    A recursive algorithm for simultaneous estimation and tracking of instantaneous frequencies and instantaneous frequency rates-of-change for signals that consist of multiple narrow-band components in noise is proposed and studied. The algorithm recursively separates the signal to individual components and uses estimated phase differences for updating the instantaneous frequency and frequency rate of each component. The main advantages of the proposed algorithm over frequencies-only tracking algorithms known in literature include the zero asymptotic bias (zero tracking delay) in estimating of the instantaneous frequencies of linear FM (chirp) signals and more accurate tracking of frequencies that cross each other. Performance of the algorithm is studied by means of a linear filter approximation technique and derived results are compared with the appropriate (posterior) Cramer-Rao bound. Superior performance of the algorithm is illustrated by computer simulations.

  • 29.
    Trump, Tõnu
    et al.
    Department of Radio and Communication Engineering, Tallinn Technical University, Tallinn, Stonia .
    Ottersten, Björn
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Estimation of Nominal Direction of Arrival and Angular Spread Using an Array of Sensors1996In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 50, no 1-2, p. 57-69Article in journal (Refereed)
    Abstract [en]

    The problem of estimating the nominal direction of arrival and angular spread of a source surrounded by a large number of local scatterers using an array of sensors is addressed. This type of propagation occurs frequently in, for example, mobile communications. The maximum likelihood estimator is considered and two computationally less complex estimators are also proposed. They are based on least-squares fits of the sample covariance to the theoretical covariance matrix derived from the measurement model. The performance of the least-squares-based algorithm is analyzed and based on this, an optimally weighted least-squares criterion is proposed. The weighted least-squares algorithm is shown to be asymptotically efficient. Results of numerical experiments are presented to indicate small sample behavior of the estimators. The nominal direction-of-arrival (DOA) estimates are compared with those provided by a standard subspace algorithm. Finally, the methods are applied to experimental array data to determine spread angles for non line of sight scenarios.

  • 30.
    Venkitaraman, Arun
    et al.
    Department of Electrical Engineering, Indian Institute of Science, Bangalore 560012, India .
    Seelamantula, Chandra Sekhar
    Indian Institute of Science Bangalore.
    Fractional Hilbert transform extensions and associated analytic signal construction2014In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 94, p. 359-372Article in journal (Refereed)
    Abstract [en]

    The analytic signal (AS) was proposed by Gabor as a complex signal corresponding to a given real signal. The AS has a one-sided spectrum and gives rise to meaningful spectral averages. The Hilbert transform (HT) is a key component in Gabor's AS construction. We generalize the construction methodology by employing the fractional Hilbert transform (FrHT), without going through the standard fractional Fourier transform (FrFT) route. We discuss some properties of the fractional Hilbert operator and show how decomposition of the operator in terms of the identity and the standard Hilbert operators enables the construction of a family of analytic signals. We show that these analytic signals also satisfy Bedrosian-type properties and that their time-frequency localization properties are unaltered. We also propose a generalized-phase AS (GPAS) using a generalized-phase Hilbert transform (GPHT). We show that the GPHT shares many properties of the FrHT, in particular, selective highlighting of singularities, and a connection with Lie groups. We also investigate the duality between analyticity and causality concepts to arrive at a representation of causal signals in terms of the FrHT and GPHT. On the application front, we develop a secure multi-key single-sideband (SSB) modulation scheme and analyze its performance in noise and sensitivity to security key perturbations.

  • 31.
    Venkitarman, Arun
    et al.
    Department of Electrical Engineering, Indian Institute of Science, Bangalore 560012, India.
    Adiga, Aniruddha
    Indian Institute of Science Bangalore.
    Seelamantula, Chandra Sekhar
    Indian Institute of Science Bangalore.
    Auditory-motivated Gammatone wavelet transform2014In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 94, p. 608-619Article in journal (Refereed)
    Abstract [en]

    The ability of the continuous wavelet transform (CWT) to provide good time and frequency localization has made it a popular tool in time-frequency analysis of signals. Wavelets exhibit constant-Q property, which is also possessed by the basilar membrane filters in the peripheral auditory system. The basilar membrane filters or auditory filters are often modeled by a Gammatone function, which provides a good approximation to experimentally determined responses. The filterbank derived from these filters is referred to as a Gammatone filterbank. In general, wavelet analysis can be likened to a filterbank analysis and hence the interesting link between standard wavelet analysis and Gammatone filterbank. However, the Gammatone function does not exactly qualify as a wavelet because its time average is not zero. We show how bona fide wavelets can be constructed out of Gammatone functions. We analyze properties such as admissibility, time-bandwidth product, vanishing moments, which are particularly relevant in the context of wavelets. We also show how the proposed auditory wavelets are produced as the impulse response of a linear, shift-invariant system governed by a linear differential equation with constant coefficients. We propose analog circuit implementations of the proposed CWT. We also show how the Gammatone-derived wavelets can be used for singularity detection and time-frequency analysis of transient signals.

  • 32.
    Werner, Karl
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jansson, Magnus
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Estimating MIMO channel covariances from training data under the Kronecker model2009In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 89, no 1, p. 1-13Article in journal (Refereed)
    Abstract [en]

    Many algorithms for transmission in multiple input multiple output (MIMO) communication systems rely on second order statistics of the channel realizations. The problem of estimating such second order statistics of MIMO channels, based on limited amounts of training data, is treated in this article. It is assumed that the Kronecker model holds. This implies that the channel covariance is the Kronecker product of one covariance matrix that is associated with the array and the scattering at the transmitter and one that is associated with the receive array and the scattering at the receiver. The proposed estimator uses training data from a number of signal blocks (received during independent fades of the MIMO channel) to compute the estimate. This is in contrast to methods that assume that the channel realizations are directly available, or possible to estimate almost without error. It is also demonstrated how methods that make use of the training data indirectly via channel estimates can be biased. An estimator is derived that can, in an asymptotically optimal way, use, not only the structure implied by the Kronecker assumption, but also linear structure on the transmit- and receive covariance matrices. The performance of the proposed estimator is analyzed and numerical simulations illustrate the results and also provide insight into the small sample behaviour of the proposed method.

  • 33.
    Wirfält, Petter
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jansson, Magnus
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Prior-exploiting Direction-of-Arrival algorithms for partially uncorrelated source signals2015In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 109, p. 182-192Article in journal (Refereed)
    Abstract [en]

    In this article, we investigate the performance of the recently proposed Direction-Of-Arrival (DOA) estimator POWDER (Prior Orthogonally Weighted Direction EstimatoR). The method is exploiting a specific form of prior information, namely that some DOAs are known, as well as that the correlation state between some of the source signals is known. In such scenarios, it is desirable to exploit the prior information already in the estimator design such that the knowledge can benefit the estimation of the DOAs of the unknown sources. Through an asymptotical statistical analysis, we find closed form expressions for the accuracy of the method. We also derive the relevant Cramér-Rao Bound, and we show the algorithm to be efficient under mild assumptions. The realizable performance in the finite sample-case is studied through numerical Monte-Carlo simulations, from which one can conclude that the theoretically predicted accuracies are attained for modest sample sizes and comparatively low SNR. This has the implication that the algorithm is significantly more accurate than other, state-of-art, methods, in a wide range of scenarios.

  • 34.
    Wolkerstorfer, Martin
    et al.
    FTW Telecommunications Research Center Vienna.
    Jaldén, Joakim
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Nordström, Tomas
    Centre for Research on Embedded Systems (CERES), Halmstad University.
    Low-complexity optimal discrete-rate spectrum balancing in digital subscriber lines2013In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 93, no 1, p. 23-34Article in journal (Refereed)
    Abstract [en]

    Discrete-rate spectrum balancing in interference-limited multi-user and multi-carrier digital subscriber lines (DSL) is a large-scale, non-convex and combinatorial problem. Previously proposed algorithms for its (dual) optimal solution are only applicable for networks with few users, while the suboptimality of less complex bit-loading algorithms has not been adequately studied so far. We deploy constrained optimization techniques as well as problem-specific branch-and-bound and search-space reduction methods, which for the first time give a low-complexity guarantee of optimality in certain multi-user DSL networks of practical size. Simulation results precisely quantify the suboptimality of multi-user bit-loading schemes in a thousand ADSL2 scenarios under measured channel data.

  • 35.
    Zachariah, Dave
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wirfält, Petter
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jansson, Magnus
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Line spectrum estimation with probabilistic priors2013In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 93, no 11, p. 2969-2974Article in journal (Refereed)
    Abstract [en]

    For line spectrum estimation, we derive the maximum a posteriori probability estimator where prior knowledge of frequencies is modeled probabilistically. Since the spectrum is periodic, an appropriate distribution is the circular von Mises distribution that can parameterize the entire range of prior certainty of the frequencies. An efficient alternating projections method is used to solve the resulting optimization problem. The estimator is evaluated numerically and compared with other estimators and the Cramer-Rao bound.

  • 36. Zaki, Ahmed
    et al.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Signal Processing.
    Rasmussen, Lars Kildehöj
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Generalized fusion algorithm for compressive sampling reconstruction and RIP-based analysis2017In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 139, p. 36-48Article in journal (Refereed)
    Abstract [en]

    We design a Generalized Fusion Algorithm for Compressive Sampling (gFACS) reconstruction. In the gFACS algorithm, several individual compressive sampling (CS) reconstruction algorithms participate to achieve a better performance than the individual algorithms. The gFACS algorithm is iterative in nature and its convergence is proved under certain conditions using Restricted Isometry Property (RIP) based theoretical analysis. The theoretical analysis allows for the participation of any off-the-shelf or new CS reconstruction algorithm with simple modifications, and still guarantees convergence. We show modifications of some well-known CS reconstruction algorithms for their seamless use in the gFACS algorithm. Simulation results show that the proposed gFACS algorithm indeed provides better performance than the participating individual algorithms.

1 - 36 of 36
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